Aircraft: MEDIUM TRANSPORT; LOW WING; 2 TURBOJET ENG
Phase of flight: Climb
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance

This occurred during the morning departure rush. I was working the departures and arrivals into the airport. This is usually combined up from XA00 until around XB00 when we have more staffing. There was Aircraft Y that departed off SJC on the SID southeast bound at 5000 feet. The next aircraft was Aircraft X who was also on the same departure. I radar identified the aircraft continued working because I had other aircraft on frequency that needed to be turned to final and on course. When I scanned again towards my departures to climb Aircraft Y I noticed that Aircraft X turned southeast bound earlier than he should have and was going to cut off Aircraft Y. I climbed Aircraft Y to 15000 feet and turned Aircraft X to a 030 heading but the loss had already occurred and he got to approximately 1.7 miles and same altitude of Aircraft Y. This increased my workload immensely because now I had to vector Aircraft X off the SID and ensure he didn't interfere with the rest of the departures that were coming off. Not even three minutes later a jet (Aircraft Z) departed also on the loupe 4 departure. I radar identified that aircraft and was still sorting out the mess with Aircraft X and turning aircraft onto the ils for runway 30L. I then saw the Aircraft Z go northbound towards the adjacent airport's finals climbing to 5000 feet. I told the aircraft to turn to a heading of 150 degress immediately. I called tower and told them to stop departures. At that point there was another aircraft airborne at the departure end and one on the roll. Now there were two more planes that are put in an unsafe situation because the pilot of the Aircraft Z did not fly the SID correctly. I had to get a pointout with the next sector; the adjacent sector north of me. Once Aircraft Z was southeast bound I had to turn him eastbound because the other airborne aircraft. I paralleled Aircraft Z with the two departures and turned Aircraft Z back toward the vor to resume the SID. I issued the brasher statement to Aircraft Z pilot and the next TRACON sector issued the brasher statement to Aircraft X. This is a common problem with this departure. Someone needs to look at the SID and possibly rewrite this so that it is easily understandable. This is not the first time that this has happened and today it happened to another coworker of mine. SJC tower is a tower with radar and responsible for successive departure separation. They have automatic releases. They should ensure that all aircraft are in the right turn prior to communications transfer. The tower does not stop departures even when there's a runaway SID departing. If the tower were made responsible to ensure the aircraft is in the turn then they would be more reluctant to keep departures going which in turn would make the airspace a lot safer. On departure I was notified that I turned to a heading of 123 degrees before 1.8 DME off VOR. If this was accurate; I would have to probably have to contribute it to fatigue to the chain of events. We we working off of the minimal 10 hour rest requirement. This was already the second leg of the day. Overall it was a 14 hour duty day. A Controller and flight crew reported the pilot flew the SID incorrectly causing conflictions with other aircraft.